Answer:
a) 2179 parkas
b) 0.7389
c) 174 customers
d) 10,772
Explanation:
Given:
Bower's selling price =$22
Salvage value: $0
Cost price = $12
Mean distribution= 2300 parkas
S.d = 1100 parkas
a) Number of parkas Teddy Bower should buy from Teddysports to maximize profit:
Let's first calculate overage(Co) and underage (Cu) cost.
•Cu = Selling price - Cost price
= $22 - $12
= $10
Underage cost = $10
•Co = Cost price - Salvage value
= $12 - $0
= $12
Overage cost = $12
Let's now find the critical ratio with the formula:
[tex] \frac{C_u}{C_u+C_o}[/tex]
[tex]= \frac{10}{12+10} [/tex]
= 0.4545
From the Excel function NORMSINV, the corresponding z value is =
NORMSINV(0.4545)
z value = -0.11
For the number of parkas Teddy Brown should order, we have:
Quantity = Mean +(z*s.d)
= 2300+ (-0.11 * 1100)
= 2179 parkas
b) for z value corresponding to expected sales of 3000 parkas, we have:
z value = (expected demand -mean)/s.d
[tex] \frac{3000-2300}{1100}[/tex]
= 0.64
From the Excel function NOEMSDIST, the corresponding probability =
NORMSDIST(0.64)
= 0.7389 = 73.89%
In stock probability = 0.7389
c) For L(0.64) using the standard normal loss function table, L(z) =
L (0.64) = 0.158
For expected lost sales, we have:
S.d * L(z)
= 1100* 0.158
= 173.8
= 174.
On average, there is expected to be a turn away of 174 customers due to shortage.
d)
Lets first calculate expected sales and left over inventory.
•Expected sales = Mean -expected lost sales
= 2,300 - 174
= 2,126
•Left over inventory expected=
Expected demand - Expected lost sales
= 3000 - 2126
= 874
For expected profit, we have:
[tex] (C_u* Expected lost sales)-(C_o* Expected leftover inventory)[/tex]
=($10*2126)-($12*874)
= $10,772
Profit expected = $10,772
